{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:DI4DQS2M6A24NVGUCPI2SJELLR","short_pith_number":"pith:DI4DQS2M","schema_version":"1.0","canonical_sha256":"1a38384b4cf035c6d4d413d1a9248b5c41cf914da0ed54d61f2d42b4bc2b4b99","source":{"kind":"arxiv","id":"1609.07305","version":3},"attestation_state":"computed","paper":{"title":"Strichartz estimates for the fractional Schr\\\"odinger and wave equations on compact manifolds without boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Van Duong Dinh","submitted_at":"2016-09-23T10:43:54Z","abstract_excerpt":"We firstly prove Strichartz estimates for the fractional Schr\\\"odinger equations on $\\mathbb{R}^d$ endowed with a smooth bounded metric $g$. We then prove Strichartz estimates for the fractional Schr\\\"odinger and wave equations on compact Riemannian manifolds without boundary $(M,g)$. We finally give applications of Strichartz estimates for the local well-posedness of the pure power-type nonlinear fractional Schr\\\"odinger and wave equations posed on $(M,g)$."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1609.07305","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-09-23T10:43:54Z","cross_cats_sorted":[],"title_canon_sha256":"69bc497eba46466aea360f0928b85ac6e0a11c628b696e8c5b30dd28853782d8","abstract_canon_sha256":"15817312eeb2d8887e6632d8fd04bf392029e0ba89acab6157cd7946254c190b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:33:00.019355Z","signature_b64":"Yw9FUZLqjZwIcyN0blrekCyT+N6RUW8n1k1PzisKwlWR/OUQ2CWXj/fbXVmOv+6fd6v9jiZUTSwr9ATGtA7jDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1a38384b4cf035c6d4d413d1a9248b5c41cf914da0ed54d61f2d42b4bc2b4b99","last_reissued_at":"2026-05-18T00:33:00.018728Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:33:00.018728Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Strichartz estimates for the fractional Schr\\\"odinger and wave equations on compact manifolds without boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Van Duong Dinh","submitted_at":"2016-09-23T10:43:54Z","abstract_excerpt":"We firstly prove Strichartz estimates for the fractional Schr\\\"odinger equations on $\\mathbb{R}^d$ endowed with a smooth bounded metric $g$. We then prove Strichartz estimates for the fractional Schr\\\"odinger and wave equations on compact Riemannian manifolds without boundary $(M,g)$. We finally give applications of Strichartz estimates for the local well-posedness of the pure power-type nonlinear fractional Schr\\\"odinger and wave equations posed on $(M,g)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.07305","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1609.07305","created_at":"2026-05-18T00:33:00.018830+00:00"},{"alias_kind":"arxiv_version","alias_value":"1609.07305v3","created_at":"2026-05-18T00:33:00.018830+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.07305","created_at":"2026-05-18T00:33:00.018830+00:00"},{"alias_kind":"pith_short_12","alias_value":"DI4DQS2M6A24","created_at":"2026-05-18T12:30:12.583610+00:00"},{"alias_kind":"pith_short_16","alias_value":"DI4DQS2M6A24NVGU","created_at":"2026-05-18T12:30:12.583610+00:00"},{"alias_kind":"pith_short_8","alias_value":"DI4DQS2M","created_at":"2026-05-18T12:30:12.583610+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/DI4DQS2M6A24NVGUCPI2SJELLR","json":"https://pith.science/pith/DI4DQS2M6A24NVGUCPI2SJELLR.json","graph_json":"https://pith.science/api/pith-number/DI4DQS2M6A24NVGUCPI2SJELLR/graph.json","events_json":"https://pith.science/api/pith-number/DI4DQS2M6A24NVGUCPI2SJELLR/events.json","paper":"https://pith.science/paper/DI4DQS2M"},"agent_actions":{"view_html":"https://pith.science/pith/DI4DQS2M6A24NVGUCPI2SJELLR","download_json":"https://pith.science/pith/DI4DQS2M6A24NVGUCPI2SJELLR.json","view_paper":"https://pith.science/paper/DI4DQS2M","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1609.07305&json=true","fetch_graph":"https://pith.science/api/pith-number/DI4DQS2M6A24NVGUCPI2SJELLR/graph.json","fetch_events":"https://pith.science/api/pith-number/DI4DQS2M6A24NVGUCPI2SJELLR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DI4DQS2M6A24NVGUCPI2SJELLR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DI4DQS2M6A24NVGUCPI2SJELLR/action/storage_attestation","attest_author":"https://pith.science/pith/DI4DQS2M6A24NVGUCPI2SJELLR/action/author_attestation","sign_citation":"https://pith.science/pith/DI4DQS2M6A24NVGUCPI2SJELLR/action/citation_signature","submit_replication":"https://pith.science/pith/DI4DQS2M6A24NVGUCPI2SJELLR/action/replication_record"}},"created_at":"2026-05-18T00:33:00.018830+00:00","updated_at":"2026-05-18T00:33:00.018830+00:00"}